Next to the podcast and the discussion linked, I also go into the subject here, discussing Hans Mommsen and here, discussing the evidence of the Intentionalist side

It can be gleaned from the discussion in the podcast thread but essentially, this debate is over and in some ways solved. New research, new evidence discovered when the Russian and Eastern European archives opened and the generational shift among historians has more or less ended this debate.

The prevailing consensus among historians of the Third Reich now can be described as something of a moderate functionalist model. Ian Kershaw has in that regard pioneered the model of "working towards the Führer". Kershaw relies on a model of the Third Reich, that relies upon Hitler in his role as the Führer as the center actors within its structure tend to gravitate towards and who do not need a direct order.

The political structure of the Third Reich must be imagined as one of competing agencies. Essentially agencies and institutions were given the same task within the Third Reich and thereby put in competition on who was able to do it better in the eyes of the Führer. Doing in better in the eyes of Hitler was a huge political asset in this structure because it meant that you or your agency would receive further political power and responsibility. Thus, the field of politics became a battleground between various agencies and institutions all trying to anticipate what Hitler wanted; they started "working toward the Führer" in the words of Kershaw.

On some occasion, Hitler would intervene in these conflicts by either giving out a new line of policy (e.g. September 1941 when he ordered the German Jews to be deported or in December 1941 when Himmler recorded "Jews / shoot as Partisans") or by rewarding an agency or institution that had fulfilled his vaguely expressed orders in a way he perceived as useful, as did often happen in the case of the SS.

To give a quick example: In 1941, the Wehrmacht together with the Foreign Office was in charge of the occupation of Serbia. Faced with a considerable uprising that threatened to confine the troops in Serbia to the urban centers and cede control of the rest of the country to the Partisans, the culprit for this situation was quickly identified as the Jews, in line with Hitler's orders on the attack on the Soviet Union in March that year during which he proposed the commissar order also relying on the same principle, that Jews were responsible for communist resistance.

Several times, the Foreign Office in Serbia together with the Wehrmacht attempted to rid themselves of the Serbian Jews by deporting them. Only during the summer 1941, deportations were not possible because the political leadership of the General Government in Poland had successfully persuaded Hitler, that there were too many Jews in Poland already.

Faced with the uprising for which they blamed the Jews and with the assumed wish of Hitler to make their territory "Jew-free", they started to emulate what they saw was happening in the Soviet Union with the Einsatzgruppen, where they knew that this was condoned by Hitler, and started shooting the male Jews of Serbia. The historical actors in Serbia radicalized their policy to murder because based on what was happening in the Soviet Union, they assumed it to be the wish of Hitler. This is what Kershaw means with "working toward the Führer".

Furthermore, recent scholarship has shifted focus a bit on the lower levels of how the so-called Final Solution was carried out. Set off by Borwning's book on the men of the Policebattailion 101, how the local perpetrators came to be perpetrators has garnered a lot of attention. For the research on how individual actors that were not necessarily convinced Nazis came to shoot hundreds and even thousands of Jews, the IvF debate offers little value. For the question, how ordinary men turned into murderers, structure as well as the wishes of Hitler only play a minor role.

And thirdly, the debate has lost its appeal through the generational shift among historians. The IvF debate has been characterized as a very German debate because it is not only about history, it is about responsibility and legacy. The majority of historians engaged in this debate were people who could remember Nazi rule in Germany, so the question if it was Hitler or the political structure of the Third Reich that had motivated the Holocaust for them was also a question about a time they could remember and about how this past was viewed in the post-war Germany they had actively experienced. This is where some of the nastiness in the debate originated and where it lost some of its appeal to a younger generation of historians.

Since a lot of what I wrote above holds up for the German situation, I decided to also ping /u/kieslowskifan who can give further inside on the US American side of things, I hope.

Sources:

• Richard Bessel, "Functionalists vs. Intentionalists: The Debate Twenty Years on or Whatever Happened to Functionalism and Intentionalism?" German Studies Review 26, no. 1 (2003).

• Ian Kershaw: "Working Towards the Führer: Reflections on the Nature of the Hitler Dictatorship" pages 103–118 from Contemporary European History, Volume 2, Issue #2, 1993; reprinted on pages 231–252 from The Third Reich edited by Christian Leitz, London: Blackwell, 1999.

• Ian Kershaw: The Nazi Dictatorship. Problems and Perspectives of Interpretation, (London, 1985, 4th ed., 2000).

• Christopher Browning: The Origins of the Final Solution : The Evolution of Nazi Jewish Policy, September 1939 – March 1942 (With contributions by Jürgen Matthäus), Lincoln : University of Nebraska Press, 2004.

Of note, the AskHistorians podcast did an episode on Intentionalism and Functionalism. The guest, /u/commiespaceinvader, has a follow-up discussion that seems relevant to your question.